After dropping sets in each of the first two rounds, the top-seeded Swiss advanced in just over an hour and a half on Centre Court on Friday.
He made only 11 unforced errors and reeled off 29 winners to Clement's 17. He left Centre Court to a rousing standing ovation.
"I get standing ovations 99 percent of the time -- doesn't matter if the performance was great or not so great," he said. "I think they're happy to see me, and they love tennis. ... But of course, when I end up winning, and they give me a reception like this, it feels good at the heart."
Federer, who is aiming for his 17th Grand Slam title and seventh at the All England Club, will play 16th-seeded Austrian Jurgen Melzer on Monday for a berth in the quarterfinals. Melzer beat Feliciano Lopez 4-6, 6-3, 6-2, 6-4.
Federer and Melzer played doubles together as juniors but have never faced each other in singles on the tour.
"I'm excited about having a weekend off, because it's been a tough first week," Federer said. "Not as tough as Isner and Mahut, of course, but still somewhat tough mentally. So I'm looking forward to Monday."
The fifth-seeded American served 28 aces to beat the German on Court 1.
Roddick, a three-time Wimbledon finalist, broke four times and saved all seven break points against him.
Roddick missed his first match point at 5-2 when he dived in vain to reach a drop shot and landed face-first on the grass. In the next game, he saved a break point and then finished with an ace on his third match point.
That sets up an intriguing fourth-round battle against 2002 champion Lleyton Hewitt. The 15th-seeded Australian, enjoying a resurgence after returning from hip surgery, advanced with a 6-3, 7-6 (9), 6-4 win over Frenchman Gael Monfils.
Hewitt saved three set points in the second-set tiebreak and pumped his right arm four times in celebration after closing out the set. Monfils fought back to stay close in the third but double-faulted to end the match.
Daniel Brands, a German ranked 98th, moved on when No. 31 Victor Hanescu of Romania stopped playing in the fifth set because of what was officially listed as a leg injury. Hanescu was cited by the chair umpire in that set for swearing and spitting toward the crowd; police arrested four people at that court, but the tournament could not verify if the episodes were related.
Tournament referee Andrew Jarrett said his office "is reviewing further information from this match."
Information from The Associated Press was used in this report.